Problems

01

Ratio and root tests

Apply the ratio test or the root test to determine whether each of the following series is absolutely convergent, conditionally convergent, or divergent.

(a) (b) (c)

Solution

04

(a)

Therefore, by the root test the series converges absolutely.

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(b)

Therefore, by the ratio test the series converges absolutely.

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(c)

Therefore, by the ratio test the series converges absolutely.

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02

Ratio and root tests

Apply the ratio test or the root test to determine whether each of the following series is absolutely convergent, conditionally convergent, or divergent.

(a) (b) (c)

Solution

09

(a)

Since , the ratio test says that the series diverges.

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(b)

Since , the root test says that the series converges.

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(c)

Since , the ratio test says that the series converges.

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